\newproblem{lay:4_1_10}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 4.1.10}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Ana Pe\~na Gil, Jan. 19th 2014} \\}{}

  % Problem statement
	Let $H$ be the set of all vectors of the form $\begin{pmatrix}3t \\ 0 \\ -7t\end{pmatrix}$, 
	where $t$ is any real number. Show that $H$ is a subspace of $\mathbb{R}^3$.
}{
   % Solution
	Let $\mathbf{u}\in H$. Then, we can write $u=\begin{pmatrix}3t \\ 0 \\ -7t\end{pmatrix} = t\begin{pmatrix}3 \\ 0 \\ -7\end{pmatrix}$.
	So $H = \mathrm{Span}\{(3, 0, -7)\}$ and $H$ is a vector subspace $\mathbb{R}^3$ because it can be generated by a vector of $\mathbb{R}^3$.
	
}
\useproblem{lay:4_1_10}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
